Gluon Saturation In Deep Inelastic Scattering

This thesis analyses gluon saturation in deep inelastic electron-proton scattering (DIS) in the light-cone gauge. It is especially convenient to introduce four kinematic variables: Q2 = -q2, xBjorken =(?) Y =(?), v =(?) . After introducing the four kinematic variables, we obtain the differential cross section at fixed Q2 and xB jorken, then the Callan-Gross rela-tion and Bjorken scaling which was first proposed by Bjorken. Afterwards, we derive and solve the DGLAP evolution equation as wel as the BFKL evolution equation. Through anal-ysis, we find that the solution to the double logarithmic approximation limit of the DGLAP evolution equation is the same as the solution to the double logarithmic approximation limit of the BFKL evolution equation.Further study find that the BFKL evolution equation vio-lates the Froissart bound. Therefore, we introduce the McLerran-Venugopalan Model and the Balitsky-Kovchegov evolution equation. The Balitsky-Kovchegov evolution equation does not violate the Froissart bound. The process of DIS materially is electron and quark included in proton interact with each other through virtual photon. We suppose that a virtual photon fluctuates into a quark-antiquark pair, which can be viewed as a pair of color dipole. When the imaginary part of the forward scattering amplitude for dipole-proton scattering N(blo1, 11o1, Y) + 1 (namely as Y + 1), the Balitsky-Kovchegov evolution equation is equivalent to the BFKL evolution equation. The condition of gluon saturation can be ob-tained by the Balitsky-Kovchegov evolution equation.Through analysis, we show that the increasing energy forces the gluons to occupy the same high momentum state (due to repulsive interactions) when the collision energy is beyond a certain limit, which weaken the strong interaction coupling. In the context of DIS, the high energy asymptotics can be explored by fixing the photon virtuality Q2 and taking the electron-proton center-of-mass energy squared s to be large. Since Q2 (s - mp) xB ,rkenY, we know that (?),The higher the electron-proton center-of-mass energy in DIS is, the smaller xBj,,rken be-comes. As xB jorken turns smaller and smaller, proton becomes more and more densely populated due to strong increase of parton number. The evolution of the gluon distribution G(x, Q2) runs much faster than that of the quark distributions (both singlet and nonsinglet), at small xBjarken- When xBj,,rken + 1, the gluon distribution G(x, Q2) becomes dominant. Eventually, proton becomes too densely populated as xB j,,rken is extremely small, the quan-tity of gluons stops to increase. It means that gluon saturation appears. When gluon satu-ration occurs, many gluons gather near the same momentum state QS, which is just similar to Bose-Einstein condensate. As a result, gluon saturation is known as the Color Glass Condensate (CGC). The gluon saturation region depends on XBjorken as well as Q2 because of the asymptotic freedom of the strong interaction coupling constant as.